A NOTE ON THE EXTENSION OF ε-ISOMETRIES ON THE UNIT SPHERE OF BANACH SPACES

ROHMAN M., ERYILMAZ İ.

HONAM MATHEMATICAL JOURNAL, no.1, pp.38-46, 2024 (ESCI) identifier

  • Publication Type: Article / Article
  • Publication Date: 2024
  • Doi Number: 10.5831/hmj.2024.46.1.38
  • Journal Name: HONAM MATHEMATICAL JOURNAL
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.38-46
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

Let X, Y be Banach spaces, S X and S Y be the unit sphere of X and Y, respectively. Let f 0 : S X -+ S Y be epsilon- isometry for some epsilon >= 0. In this paper, we show that there is an extension f : X -+ Y of f 0 such that f is linear.